Session I.5 - Geometric Integration and Computational Mechanics
Poster
Symplectic groupoids for Poisson integrators
Oscar Cosserat
CNRS/La Rochelle Université, France - This email address is being protected from spambots. You need JavaScript enabled to view it.
Geometric technics are developed to build Hamiltonian Poisson integrators for generic Hamiltonian and Poisson structure. Such technics allow to compute precise estimates on the error and are theoretical tools to understand better the stability of such integrators on long run simulations. The main geometric object is the local symplectic groupoid of the considered Poisson structure. Those technics are illustrated on rigid body dynamics and Lotka-Volterra equations. The poster is based on the following preprints : Symplectic Groupoids for Poisson Integrators, O. C., arXiv:2303.15883 Numerical Methods in Poisson Geometry and their Application to Mechanics , O. C., C. Laurent-Gengoux, V. Salnikov, arXiv:2205.04838
Joint work with Camille Laurent-Gengoux (Institut Élie Cartan de Lorraine, France) and Vladimir Salnikov (CNRS/La Rochelle Unviersité, France).